Q. If $A$ and $B$ are two square matrices such that $B = - A^{- 1}\ BA$, then $(A + B)^{2}$ is equal to
A) $A^{2} + B^{2}$
B) O
C) $A^{2} + 2AB + B^{2}$
D) $A + B$
Explanation
(a)
As $B = - A^{1}BA$, we get
$AB = - BA\ \$or$\ AB + BA = 0$
Now,
$(A + B)^{2} = (A + B)(A + B)$
$= A^{2} + BA + BA + B^{2}$
$= A^{2} + 0 + B^{2}$
$= A^{2} + B^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.